Social networking sites such as Facebook and Twitter have rapidly become a mainstream medium. The spanner in the works of their incredible rise is now the landmark case of Ryan Giggs suing Twitter for breach of an injunction. This issue has nothing to do with whether or not public figures should be able to gag the media through injunctions and superinjunctions – whether 75,000 Twitter users, as the Lib Dem MP John Hemming used parliamentary privilege to point out, should be allowed to gossip about a footballer or not is irrelevant.

It's wholly to do with whether social networking sites such as Facebook and Twitter – massive revenue earning organisations – should operate outside the law that affects everybody else. In their defence, they will argue that they are merely providing a platform or a blank sheet of paper for users.

For a long time, the left wing has tried to uphold a parallel faith in the right to freedom of speech and the right to privacy – a contradiction that is now under more strain than ever. It's not something Nicolas Sarkozy is going to sort out in his two-day technology forum prior to the G8 meeting with chiefs from Facebook, Google and Amazon.

What flies in the face of all their likely arguments is that social networks like Facebook and Twitter, just like traditional media, sell their audiences to advertisers – cut up by user preferences and with IP address data telling advertisers where those audiences are. With Twitter currently in the process of opening a London office to directly target UK advertisers, they should particularly fall in line with UK law.

Social networks can't have it both ways. Unless we decide to become an anarchistic society, Facebook and Twitter must be reeled in. If it's not the Ryan Giggs's legal action against Twitter that does it, it will be the next alleged sexual scandal that a public figure uses the courts to prevent being published.

The central point here is whether Twitter and Facebook, as publishers of content, should be as accountable as traditional media. The problem is one of scale. Traditional media controls its content by employing finite numbers of staff, freelance journalists and news agencies. In contrast, Facebook have an army of "citizen journalists" numbering 500 million and Twitter 175 million and don't employ any of them.

Clearly, they are going to have to introduce a delay mechanism so that content can be checked before it goes up. There will have to be a completely different structure, which will be difficult when the whole thing about Twitter is its spontaneity.

Celebrities now need to disclose their commercial interests when they tweet, so we can see the same rules of product placement already being applied to the social media environment as to traditional media. It's not a matter of whether social networking is forced to grow up, but just when it will grow up.

Twitter and Facebook are not blank sheets of paper. They are media publishers like any other. Social networking at the moment is like a pioneering goldrush; a real land grab. We have to get some sort of international arbitration set up, which the Americans would need to be involved in, and quickly.

• This article was amended on 25 May 2011. It originally referred to Ryan Giggs suing Twitter for breaching a superinjunction. Lord Neuberger's report has made it clear that the term 'superinjunction' should be reserved for orders that the media cannot mention, and not used for anonymised privacy injunctions. This has now been corrected